m1_practice_soln - ECE 562 Fall 2011 PRACTICE EXAM 1...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ECE 562 Fall 2011 PRACTICE EXAM 1 Solutions 1. (15 pts total) True or False. Determine if the following statements are True or False. You need to provide a brief justification for your answer to get credit. (a) The complex baseband representation of 2 cos( t ) cos(2 f c t ) is cos( t ). Ans: True. By the definition of the complex baseband representation. (b) If X = X I + jX Q is a proper complex random variable then Var( X I + X Q ) = Var( X I ) + Var( X Q ) Ans: True. Since X I and X Q are uncorrelated. (c) The maximum likelihood detector always minimizes the error probability. Ans: False. Only if the symbols are equally likely. (d) For PSK modulation on an AWGN channel, the Intelligent Union Bound and Nearest Neighbor Approximation always coincide. Ans: True. The nearest neighbors cover the entire error region. (e) For 4-ary orthogonal modulation, P b = P e / 2. Ans: False. P b = 2 3 P e 2. (11 pts total) Gram-Schmidt. Consider the following signal set. t s 3 ( t ) s 1 ( t ) s 2 ( t ) 1 2 t 1 1 t 1 1 2 t 1 1 2 1 s 4 ( t ) (a) (4 pts) Find an orthonormal basis for the span of this signal set. (Think before you answer since the G-S solution is not unique.)you answer since the G-S solution is not unique....
View Full Document

This document was uploaded on 02/08/2012.

Page1 / 3

m1_practice_soln - ECE 562 Fall 2011 PRACTICE EXAM 1...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online